Nontrivial solutions of nonlocal fourth order elliptic equation of Kirchhoff type in R3

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:459

Article

Mao, Anmin¹  Wang, Wenqing¹ 

[1] Qufu Normal Univ, Sch Math Sci, Jining 273165, Shandong, Peoples R China

关键词: Bi-harmonic operator;    Concave and convex terms;    Sign-changing potential;   

DOI  :  10.1016/j.jmaa.2017.10.020

来源: Elsevier

【 摘 要 】

This paper is devoted to a class of important and general nonlocal fourth order elliptic problem Delta(2)u - (1 + lambda integral vertical bar del u vertical bar(2)dx)Delta u + V(x)u = f(x, u) in R-3, where Delta(2) = Delta(Delta) is the bi-harmonic operator, lambda >= 0 is a constant. We focus on the case that f (x, u) involves a combination of convex and concave terms and the potential V(x) is allowed to be sign-changing. By new techniques, multiplicity results of two different type of solutions are established. Our results improves and generalizes that obtained in the literature. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free